This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
Search for it once you enter Darril's Tomb (which only appears once you
reach the World of Ruin).
To find it, keep moving through the tomb until you find a room with four
graves. Read all four graves, then head back to near the beginning. In
the hallway where you began, in the door on the upper-left is a room
with a blank grave.
The four words from the tombstones will appear, and you need to make a
sentence using them. .sdrawkcab knihT :tniH
If you got the puzzle right, the location of the Experience Egg will be
revealed to you.
Mental block today? If so, read on...
From the beginning, head left down the entry hall, turn down (south), go
downstairs. Search the right wall.